End Behavior of Exponential Functions

Front

What is the transformation of the function f(x) = 2(4)^(x + 5)?

Back

Left 5

Front

Identify the common ratio (multiplier) of the function f(x) = 2(4)^(x).

Back

4

Front

What is the end behavior on the right side of the exponential function f(x) = 2(4)^(x)?

Back

As x → ∞, y → ∞

Front

What is the end behavior on the left side of the exponential function f(x) = 2(4)^(x)?

Back

As x → -∞, y → 0

Front

Which of the following is an exponential decay model? y = 3 * (1/2)^(x), y = 1/2 * (3)^(x), y = -2 * (2)^(x), y = -3 * (3/2)^(x)

Back

y = 3 * (1/2)^(x)

Front

What is an exponential function?

Back

A function of the form f(x) = a * b^(x), where a > 0, b > 0, and b ≠ 1.

Front

What does it mean for a function to have exponential growth?

Back

The function increases rapidly as x increases, typically when the base b > 1.

Front

What does it mean for a function to have exponential decay?

Back

The function decreases rapidly as x increases, typically when the base 0 < b < 1.

Front

How does the graph of an exponential function behave as x approaches negative infinity?

Back

The graph approaches the x-axis (y = 0) but never touches it.

Front

What is the y-intercept of the function f(x) = 2(4)^(x)?

Back

The y-intercept is (0, 2 * 4^0) = (0, 2).